Rapid Revision · Quantitative Aptitude
One idea runs the whole chapter: rate of work. Pick the total work as an LCM number and every question becomes small-number arithmetic.
If you read nothing else tonight, read these 6 lines.
Every formula for time & work in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
One day's work
if the whole job takes n days, 1 day = 1/n of it
Work together
together = (a x b) / (a + b) days
A alone a days, B alone b days. Extends by adding 1/c, 1/d...
Rate x time
work done = rate x time
Men-days equivalence
(M1 x D1 x H1) / W1 = (M2 x D2 x H2) / W2
Efficiency
efficiency is inversely proportional to time
A twice as fast as B => A:B time = 1:2, work = 2:1.
Pipes & cisterns
fill pipe = +1/a, leak = -1/b (same 1/n logic, leaks are negative)
7 cards, each one idea: what it is, a worked example, and the trap to dodge.
Set total work = LCM of the given day-counts. Each worker's rate becomes a whole number of units per day; add and divide.
A in 12 days, B in 6: work = 12 units, rates 1 and 2, together 12/3 = 4 days.
Trap: Fractions like 1/12 + 1/6 work too, but unit counting is faster and safer under pressure.
Twice as efficient means half the time. Efficiency ratio a:b implies time ratio b:a.
A is twice as fast as B; together they take 18 days. Rates 2x + x = 1/18, so x = 1/54: A alone = 27 days.
M1 x D1 x H1 / W1 = M2 x D2 x H2 / W2. More men or hours means fewer days for the same work.
10 men, 8 days for one wall; 4 men for two walls: D = 10 x 8 x 2 / 4 = 40 days.
Trap: Keep work on its own side; doubling work doubles the right-hand side.
Split the timeline. Count units done while everyone worked, then let the remaining workers finish the leftover units.
A(12d) and B(6d) start together (3 units/day on 12 units); B leaves after 2 days: 6 units left, A alone finishes in 6 more days.
Compute one full cycle (for example A's day + B's day), multiply cycles until close to the total, then finish day by day.
A does 2 units/day, B does 1, work 10 units, A starts: each 2-day cycle = 3 units; after 3 cycles (9 units, 6 days), A finishes 1 unit in half a day: 6.5 days.
Trap: Whose turn it is on the final partial day changes the answer; track the order.
Inlets add work, outlets subtract. Net rate = 1/fill - 1/drain, with the same LCM trick.
Fills in 6 h, leak empties in 8 h: net = 1/6 - 1/8 = 1/24, so 24 hours.
Trap: If the drain is faster than the fill, the tank never fills; check signs before solving.
Payment divides in the ratio of work DONE, which is the ratio of rates when time is equal.
A(6d) and B(12d) finish a job together; wages 900 split 2:1 = 600 and 300.
A recap is not practice. These are the creators we rate for real depth on time & work; full credit to each.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.